Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables (r.v.), respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forward- or backward-coupling in Straka and Henry (2011) [37] using marked point processes. We also establish a series representation for the different limits. The methods used also allow us to solve an open problem concerning residual order statistics by LePage (1981) [20].     

Mechanisms of Cobalt/Phosphine-Catalyzed Cross-Coupling Reactions

>The combination of CoCl₂ with bidentate phosphines is known to catalyze challenging cross-coupling and Heck-type reactions, but the mechanisms of these valuable transformations have not been established. Here, we use electrospray-ionization mass spectrometry to intercept the species formed in these reactions. Our results indicate that a sequence of transmetalation, reductive elimination, and redox disproportionation convert the cobalt(II) precatalyst into low-valent cobalt complexes. These species readily transfer single electrons to alkyl bromides, which thereupon dissociate into alkyl radicals and Br⁻. In cross-coupling reactions, the alkyl radicals add to the cobalt catalyst to form observable heteroleptic complexes, which release the coupling products through reductive eliminations. In the Heck-type reactions, the low abundance of newly formed ionic species renders the analysis more difficult. Nonetheless, our results also point to the occurrence of single-electron transfer processes and the involvement of radicals in these transformations.     

Physical Dimensions/Units and Universal Constants: Their Invariance in Special and General Relativity

The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing mechanics and electrodynamics, it naturally leads one, besides the dimensions of length and time, to the fundamental units of action $\mathfrak{h}$, electric charge q, and magnetic flux ?. Also, $q\times ?=\text{action}$ and $q/?=1/\text{resistance}$ are known. These results of classical physics suggests to look into the corresponding quantum aspects of q and ? (and also of $\mathfrak{h}$): The electric charge occurs exclusively in elementary charges e, whereas the magnetic flux can have any value; in specific situations, however, in superconductors of type II at very low temperatures, ? appears quantized in the form of fluxons (Abrikosov vortices). And $\mathfrak{h}$ leads, of course, to the Planck quantum h. Thus, one is directed to superconductivity and, because of the resistance, to the quantum Hall effect. In this way, the Josephson and the quantum Hall effects come into focus quite naturally. One goal is to determine the behavior of the fundamental constants in special and in general relativity.     

The Determination Of Sub Part-Per-Billion Levels Of Volatile Organic Compounds In Air By Pre-Concentration From Small Sample Volumes

Abstract

Trace level Volatile Organic Compounds (VOCs) in ambient air are normally determined according to EPA Method TO-14. This method describes the analysis in ambient air of 41 VOCs, ranging in boiling point from -29 to 215°C. It covers a concentration range from 0.2 to 20 parts per billion, volume/volume (ppb), and specifies sample enrichment of a 400 mL air sample on glass beads at -160°C. While this sample volume provides sub-ppb levels of VOC detection for target analytes when using a quadrupole mass spectrometer detector in SIM mode or when using GC detectors, the identification of non-target analytes may only be done in full scan mode for higher concentrations. Also with this sample volume a Nafion dryer is needed for water removal thereby lowering the recovery of polar VOCs.

Because of the very high sensitivity of the ion trap MS, relatively small air volumes (60 mL) are adequate to obtain the required or lower detection levels. An integrated air analysis system based on a GC-ion-trap MS has been investigated and is described. This system has a built-in cryogenic trap and necessary valving, internal standard gas sampling loop, and is controlled from the GC-MS workstation. The linearity, precision, and method detection levels obtainable with this system when using small volumes are reported. In addition, examples of the quantitative and qualitative analysis of ambient air samples are shown.     

Highly Conjugated π-Systems Arising from Cannibalistic Hexadehydro-Diels–Alder Couplings: Cleavage of C−C Single and Triple Bonds

We have investigated the cannibalistic self-trapping reaction of an ortho-benzyne derivative generated from 1,11-bis(p-tolyl)undeca-1,3,8,10-tetrayne in an HDDA reaction. Without adding any specific trapping agent, the highly reactive benzyne is trapped by another bisdiyne molecule in at least three different modes. We have isolated and characterized the resulting products and performed high-level calculations concerning the reaction mechanism. During the cannibalistic self-trapping process, either a C≡C triple bond or an sp–sp³ C−C single bond is cleaved. Up to seven rings and nine C−C bonds are formed starting from two 1,11-bis(p-tolyl)undeca-1,3,8,10-tetrayne molecules. Our experiments and calculations provide considerable insight into the variety of reaction pathways which the ortho-benzyne derivative, generated from a bisdiyne, can take when reacting with another bisdiyne molecule.